Properties

Level $22$
Weight $0$
Character 22.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 7.65008673054 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.082794788\) \(a_{4}=+0.500000000\) \(a_{5}=+1.523996342\)
\(a_{6}=-0.765651537\) \(a_{7}=-1.935710873\) \(a_{8}=-0.353553391\) \(a_{9}=+0.172444553\) \(a_{10}=-1.077628148\)
\(a_{11}=-0.301511345\) \(a_{12}=+0.541397394\) \(a_{13}=-0.459750672\) \(a_{14}=+1.368754285\) \(a_{15}=+1.650175296\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.305177060\) \(a_{18}=-0.121936713\) \(a_{19}=+0.051558441\) \(a_{20}=+0.761998171\)
\(a_{21}=-2.095977645\) \(a_{22}=+0.213200716\) \(a_{23}=-0.736343033\) \(a_{24}=-0.382825769\) \(a_{25}=+1.322564849\)
\(a_{26}=+0.325092818\) \(a_{27}=-0.896072725\) \(a_{28}=-0.967855437\) \(a_{29}=+0.658876062\) \(a_{30}=-1.166850142\)
\(a_{31}=-0.066359776\) \(a_{32}=-0.176776695\) \(a_{33}=-0.326474912\) \(a_{34}=+0.922899549\) \(a_{35}=-2.950016290\)
\(a_{36}=+0.086222276\) \(a_{37}=+0.288495845\) \(a_{38}=-0.036457323\) \(a_{39}=-0.497815631\) \(a_{40}=-0.538814074\)
\(a_{41}=-0.645772844\) \(a_{42}=+1.482080006\) \(a_{43}=+0.346557750\) \(a_{44}=-0.150755672\) \(a_{45}=+0.262804868\)
\(a_{46}=+0.520673152\) \(a_{47}=-1.338630275\) \(a_{48}=+0.270698697\) \(a_{49}=+2.746976585\) \(a_{50}=-0.935194574\)
\(a_{51}=-1.413238917\) \(a_{52}=-0.229875336\) \(a_{53}=-0.736403396\) \(a_{54}=+0.633619100\) \(a_{55}=-0.459502186\)
\(a_{56}=+0.684377143\) \(a_{57}=+0.055827211\) \(a_{58}=-0.465895732\) \(a_{59}=+0.097591202\) \(a_{60}=+0.825087648\)
\(a_{61}=-1.595499159\) \(a_{62}=+0.046923448\) \(a_{63}=-0.333802796\) \(a_{64}=+0.125000000\) \(a_{65}=-0.700658342\)
\(a_{66}=+0.230852624\) \(a_{67}=-1.230410389\) \(a_{68}=-0.652588530\) \(a_{69}=-0.797308398\) \(a_{70}=+2.085976523\)
\(a_{71}=+1.335828435\) \(a_{72}=-0.060968356\) \(a_{73}=+1.373987829\) \(a_{74}=-0.203997368\) \(a_{75}=+1.432066326\)
\(a_{76}=+0.025779220\) \(a_{77}=+0.583638788\) \(a_{78}=+0.352008808\) \(a_{79}=-0.446601856\) \(a_{80}=+0.380999085\)
\(a_{81}=-1.142707429\) \(a_{82}=+0.456630357\) \(a_{83}=-1.768143821\) \(a_{84}=-1.047988822\) \(a_{85}=-1.989085064\)
\(a_{86}=-0.245053335\) \(a_{87}=+0.713427566\) \(a_{88}=+0.106600358\) \(a_{89}=+1.376696066\) \(a_{90}=-0.185831104\)
\(a_{91}=+0.889944374\) \(a_{92}=-0.368171517\) \(a_{93}=-0.071854020\) \(a_{94}=+0.946554545\) \(a_{95}=+0.078574875\)
\(a_{96}=-0.191412884\) \(a_{97}=-0.813453390\) \(a_{98}=-1.942405771\) \(a_{99}=-0.051993989\) \(a_{100}=+0.661282425\)

Showing 100 of 262 available coefficients

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